Mr. Perfect can mow his lawn efficiently, that is, he can mow his whole lawn in a continuous line from start to finish without having to go over an already mown part, as shown by the blue path below.

No matter how hard he tries, Mr. Mediocre cannot mow his lawn (shown below) as efficiently as Mr. Perfect can. A friend suggests that Mr. Mediocre plant a shrub somewhere to change the layout of his yard.

Where should Mr. Mediocre plant the shrub so that he can mow his lawn efficiently?

Assumptions:

The lawnmower can only move straight through a square or make one right angle in the square.

The lawnmower cannot move diagonally between squares.

After the lawnmower enters and exits a square, all of the grass in the square is cut.

Bonus: Prove that before he plants the shrub, it is impossible for Mr. Mediocre to mow his lawn efficiently.